I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 800 pounds more than each of her trucks, but no more than \(\frac{1}{5}\) of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?
+237 We have two conditions
Let x = the load of your teuck
and y = load of their trucks then
1) x ≥ y + 800 .... (1)
4y = the total load of their trucks
(1/5) * 4y = the load of your truck
2) 4/5 * ≤ y .... (2)
Calculations:-
x = y + 800 .... (1)
x = 5y/4 .... (2)
Put value of (2) in (1) so
5y/4 = y + 800
=> 5y/4y - y = 800
=> 1/4y = 800
=> y = 3200 pounds
then put y = 3200 in (2)
x = 5/4 (3200)
x = 4000 pounds
4000 pounds is the greatest load that your truck carry
